Problem 1. (6 points in total) Consider the following data 0.5 I; | 0 0.1 0.2 0.3 0.4 Yi 22.20254 2.40715 2.61592 2.83096 3.05448 (1) (2 points) Using least squares approximation with linear polynomial basis functions {1, x} to fit the data in the table, give the system in matriz form Ac=y. (2) (2 points) Using least squares approximation with basis functions {1,6", -1} to fit the data in the table, give the system in matrix form Ac=y. (3) (2 points) Using MATLABC=A\y to calculate in Problem 1 (1) and (2). Compare the root-mean-square (RMS) residual ||T - AC|2/16 of systems in Problem 1 (1) and (2). Problem 1. (6 points in total) Consider the following data 0.5 I; | 0 0.1 0.2 0.3 0.4 Yi 22.20254 2.40715 2.61592 2.83096 3.05448 (1) (2 points) Using least squares approximation with linear polynomial basis functions {1, x} to fit the data in the table, give the system in matriz form Ac=y. (2) (2 points) Using least squares approximation with basis functions {1,6", -1} to fit the data in the table, give the system in matrix form Ac=y. (3) (2 points) Using MATLABC=A\y to calculate in Problem 1 (1) and (2). Compare the root-mean-square (RMS) residual ||T - AC|2/16 of systems in Problem 1 (1) and (2)